A Coarse-Grained Molecular Dynamics Description of Docetaxel-Conjugate Release from PLGA Matrices

Despite the extensive use of poly-lactic-glycolic-acid (PLGA) in biomedical applications, computational research on the mesoscopic characterization of PLGA-based delivery systems is limited. In this study, a computational model for PLGA is proposed, developed, and validated for the reproducibility of transport properties that can influence drug release, the rate of which remains difficult to control. For computational efficiency, coarse-grained (CG) models of the molecular components under consideration were built using the MARTINI force field version 2.2. The translocation free energy barrier ΔGt* across the PLGA matrix in the aqueous phase of docetaxel and derivatives of varying sizes and solubilities was predicted via molecular dynamics (MD) simulations and compared with experimental release data. The thermodynamic quantity ΔGt* anticipates and can help explain the release kinetics of hydrophobic compounds from the PLGA matrix, albeit within the limit of a drug concentration below a critical aggregation concentration. The proposed computational framework would allow one to predict the pharmacological behavior of polymeric implants loaded with a variety of payloads under different conditions, limiting the experimental workload and associated costs.


S1.1. Polymer chain properties and setup.
The radius of gyration Rg of the polymer chain is defined as the root mean square of the distance of all n atoms from their COM (center of mass) according to where $ and %*' denote the position vectors of the first and COM atoms in the polymer chain, respectively. The end-to-end distance Re, between the start and the end of the polymer, is defined according to where (  Finally, in a theta Q solvent (v = 1/2), the polymer behaves as an ideal chain (random walk coil) due to comparable monomer-monomer and monomer-solvent interactions. 1 S1.2 PLGA/PEG miscibility. The PLGA/PEG miscibility trend was measured by looking at the number of interspecies contacts c in the mixtures. This quantity was estimated over time using the GROMACS routine "gmx mindist", setting a threshold distance of 0.6 nm.
The superscript refers to the n th multiplicity. PLGA chains were first quantified for two different degrees of polymerization, namely N = 16 and 64. Results obtained at the coarse-grained level using the three mapping schemes above ((S)Na-Na, Na-N0, P1-C5) were systematically compared with data obtained using the atomistic model ( Table   S1). The density values for the pure PLGA16 samples were 1.35±0.003 and 1.217±0.05 g/cm 3 at CG and UA resolution, respectively. For higher molecular weights, PLGA64, samples retuned slight larger values with equal to 1.37±0.07 and 1.27±0.003 g/cm 3 at CG and UA resolution, respectively.
Overall the difference between the CG and UA predictions amounts to ~ 0.1 g/cm 3 , which is <10%.
Notably, such a small difference was also documented for the other two parameters, radius of gyration Rg and end-to-end distance Re, in the case of PLGA16 and PLGA64 samples, regardless of the mapping type (Table S1). Multiple factors could contribute to explain this minor discrepancy. According to the 4:1 MARTINI mapping scheme (v2.2), 4 heavy atoms in the atomistic model are represented by one bead in the coarse-grained model. In our model, a standard size CG bead maps instead the 5 heavy atoms of the group XL. Additionally, the standard size MARTINI bead has a larger radius than the chemical group XG that it accommodates. This in turn causes a slight interpenetration of neighboring CG beads when their bond length is assigned to map the atomistic distance between XG and XL COMs, promoting an artificial increased beads affinity and a partial collapse of the chain.
Finally, the methyl group in the LA monomer likely disfavors chain packing as the experimental increased density of PLGA with the glycolic content suggest 2 , but this effect is expected to smooth when the system is modeled at CG resolution. As an alternative, a smaller size bead (S type) was employed to map the XG monomer. When PLGA chains were built using a dimeric SNa-Na unit, the resulting density values for pure PLGA16 and PLGA64 coarse-grained samples were approximately equal to ≈1.1, which is 0.1 g cm -3 lower than the estimated values from atomistic simulations of similar systems configurations (see Table S1).    unlike acetone ( values above 1/2) for PLGA. A value lower than 1/3 for a polymer dissolved in water or acetone has been attributed to finite size effects and already discussed elsewhere by the authors 3 . According to the empirical "like dissolves like" rule, an ideal solubility of PLGA in acetone would have been expected for the Na-Na dimer model, considering also that the chain and the solvent are both made by Na type beads. This unexpected, suboptimal solubility of PLGA in acetone at the CG level ( =0.44 ± 0.01), conversely to the atomistic case ( = 0.58 ± 0.003), must be attributed to the slight interpenetration of adjacent beads, as described above, that would cause a partial collapse of the chain. The discrepancies between the values estimated at atomistic and coarse-grained levels are narrow for PLGA chains modeled with a dimeric P1-C5 unit (Figure S2C), as compared to the alternative Na-Na and Na-N0 cases (Figures S2B and S2D). The more hydrophilic P1 beads, as compared to the Na type beads, likely contributed to reduce the artificial intrachain higher affinity and the partial collapse of the chain. Finally, the miscibility of PLGA and PEG was also estimated at CG level and compared with the atomistic results. First, the three alternative mapping schemes for PLGA were tested to check for the   The miscibility regimes previously characterized at the atomistic level are instead poorly reproduced when using the alternative dimeric P1-C5, Na-N0 and (S)Na-Na configurations ( Figure S4). In the case of the combination (S)Na-Na, the PLGA-PEG miscibility trend was not reproduced as a likely consequence of the recently emerged undesired effects rising when mixing particles of different sizes described elsewhere. 5 Figure S4. PLGA/PEG miscibility at coarse-grained resolution (4 mapping schemes